Asset portfolio tracking

ABSTRACT

Techniques are provided for adjusting a portfolio of financial assets in order to properly track the performance of a desired index. The techniques generally involve calculating a correlative value for the portfolio, and obtaining a correlative value for the index, relative to each of a number of different factors having data values that are likely to be correlated with an aggregate market value for the portfolio, where the correlative value for an item relative to a given factor is a measure of a tendency of the aggregate market value of the item to change based on a change in the data value for such factor (e.g., in the nature of a sensitivity or elasticity). Then, the portfolio is adjusted in an attempt to move its correlative profile closer to the correlative profile of the index.

This is a continuation-in-part of commonly assigned U.S. patentapplication Ser. No. 09/692,748, filed on Oct. 19, 2000 now U.S. Pat.No. 7,337,135, and titled “Asset Price Forecasting” (the '748Application), which is a continuation-in-part of commonly assigned U.S.patent application Ser. No. 09/615,025, filed on Jul. 13, 2000 now U.S.Pat. No. 6,907,403, and titled “Identifying Industry Sectors UsingStatistical Clusterization” (the '025 Application). The '748 Applicationand the '025 Application are incorporated by reference herein as thoughset forth herein in full.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention pertains to techniques for tracking an index orother portfolio and is particularly applicable to automated techniquesfor facilitating the management of an index fund or similar stockportfolio where the investment strategy is to emulate a widely followedindex.

2. Description of the Related Art

Many conventional mutual fund companies have at least one mutual fundthat attempts to track or emulate the performance of a widely followedindex, such as the S&P 500. While such an investment strategy may seemstraightforward on its face, there often are many practical problems inactively managing a fund (or other portfolio) so as to properly track abroad index.

For instance, mutual funds typically are open-ended funds that mustcontend with the individual investors purchasing and selling theirinterests in the fund. By maintaining a certain amount of cash on hand,the fund often may be able to accommodate such exits and entries.However, in cases where the total amount invested is increasing ordecreasing in significant amounts, the fund manager often will berequired to purchase additional stocks or sell some of the stocks fromthe portfolio in response to the corresponding inflow or outflow ofcash. While the amounts of such cash often will be sufficient tonecessitate the purchasing or selling assets, such amounts rarely willbe significant enough to warrant a proportionate purchase or sale of allof the stocks in the tracked index, across the board. Accordingly, thefund manager must identify a subset of the index stocks to buy or sell.Until now, no adequate conventional technique has existed forsystematically identifying such an appropriate subset of stocks (orother assets).

The foregoing situation is even further exacerbated in a situation wherea manager is given the task of tracking such a broad index whilemanaging a fund that is not sufficiently large to justify maintainingproportionate holdings of all assets in the subject index. In this case,a smaller set of assets must be selected, even at the outset, tosimulate the index. Often, this set of assets then must be adjusted overtime to reflect changes in: the value of the fund, the composition ofthe index itself, and the variations in the values of the individualassets in both the fund and the index.

SUMMARY OF THE INVENTION

The present invention addresses these problems by providing techniquesfor adjusting a portfolio of financial assets in order to properly trackthe performance of a desired index. Such techniques generally involvecalculating a correlative value for the portfolio, and obtaining acorrelative value for the index, relative to each of a number ofdifferent factors having data values that are likely to be correlatedwith an aggregate market value for the portfolio, where the correlativevalue for an item relative to a given factor is a measure of a tendencyof the aggregate market value of the item to change based on a change inthe data value for such factor (e.g., in the nature of a sensitivity orelasticity). Then, the portfolio is adjusted in an attempt to move itscorrelative profile closer to the correlative profile of the index Thus,in one aspect the invention is directed to modifying a portfolio ofassets to track an index of assets. Initially, a set of factors havingdata values that are likely to be correlated with an aggregate marketvalue for at least one of the portfolio or the index are identified.Preferably, a minimum of 5-10 and, more preferably, 18 different factorsare used. Such factors preferably include, for example, a price index,an interest rate indicator, an inflation rate indicator and a stockindex. For each of the factors, a correlative value is calculated forthe portfolio relative to such factor, thereby obtaining a correlativeprofile for the portfolio, and a correlative value is obtained for theindex relative to such factor, i.e., a correlative profile for theindex. A measure of divergence between the correlative profile for theportfolio and the correlative profile for the index is then calculated,and the portfolio is modified by buying and/or selling assets so as tominimize the measure of the divergence between the correlative profilefor the portfolio and the correlative profile for the index, subject toany other constraints. According to this aspect of the invention, thecorrelative value for an item relative to a given factor is a measure ofa tendency of the aggregate market value of the item to change based ona change in the data value for such factor.

By utilizing correlative profiles in the foregoing manner, the presentinvention often can more efficiently track (or emulate the performanceof) a target index. That is, both the process for determining whichassets to purchase or sell and the transactions themselves can be moreefficient than is possible with conventional techniques. The techniquesof the present intention are useful in a variety of different contexts,such as: for determining what transactions to perform when a portfoliois being managed to track an index and it becomes necessary to putadditional cash into the portfolio or to take cash out of the portfolio;for modifying a portfolio that is being managed to track an index whenit becomes necessary to respond to other (e.g., external) factors; formodifying an existing portfolio in connection with a decision to modifythe portfolio's investment strategy so as to begin tracking a specifiedindex; or for creating an entirely new portfolio that is intended totrack a specified index.

In specific embodiments, the foregoing process is performed by:sequentially optimizing individual transactions, executing atree-searching technique and/or pre-identifying smaller subsets ofassets from which an appropriate combination of transactions may beselected.

The foregoing summary is intended merely to provide a brief descriptionof the general nature of the invention. A more complete understanding ofthe invention can be obtained by referring to the claims and thefollowing detailed description of the preferred embodiments inconnection with the accompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow diagram illustrating the generation and use of anaggregate portfolio risk measure according to a representativeembodiment of the present invention.

FIG. 2 is a flow diagram illustrating the generation and use ofindividual ETA® divergences according to a representative embodiment ofthe present invention.

FIG. 3 is a flow diagram illustrating a technique for tracking an indexor other portfolio according to a first representative of the embodimentof the present invention.

FIGS. 4A-D graphically illustrate the problem of tracking an index ETA®profile by attempting to move the ETA® profile for a managed portfoliocloser toward the ETA® profile for the index being tracked.

FIG. 5 is a flow diagram illustrating a tree-searching technique fortracking an index or other portfolio according to a secondrepresentative of the embodiment of the present invention.

FIG. 6 is a flow diagram illustrating a technique for generating newstates for the tree-searching in the process of FIG. 5.

FIG. 7 is a state diagram illustrating the generation and pruning of newstates according to the technique shown in FIG. 6.

FIG. 8 is a flow diagram illustrating a technique for tracking an indexor other portfolio according to a third representative of the embodimentof the present invention, by first identifying multiple potentialsubsets of the available assets and examining each such subset.

FIG. 9 is a flow diagram illustrating a technique for adjusting aportfolio in order to properly track an index or other portfolio,independent of any cash-flow needs.

FIG. 10 is a flow diagram showing a technique according to the presentinvention for assessing the performance of a portfolio in comparison tothe performance of an index.

FIG. 11A graphically illustrates conventional techniques for assessingthe performance of a portfolio in comparison to the performance of anindex, while FIG. 11B illustrates a technique according to a secondembodiment of the present invention for assessing the performance of aportfolio in comparison to the performance of an index.

FIG. 12 is a flow diagram showing the technique according to the secondembodiment of the present invention for assessing the performance of aportfolio in comparison to the performance of an index.

DESCRIPTION OF THE PREFERRED EMBODIMENT(S)

The present disclosure covers inventions that are claimed in multipleconcurrently filed patent applications. Also filed concurrently herewithare the following commonly assigned patent applications: “AssetPortfolio Evaluation” and “Potential-Based Asset Comparison”, whichapplications are incorporated herein by reference as though set forthherein in full.

The following description includes aspects of the assignee's ETA® systemfor asset evaluation, forecasting, reporting and screening.

One significant application of the present invention is the comparisonof a portfolio (e.g., a portfolio being managed) to another portfolio orindex. As used herein, the term “index” when used in connection with abenchmark that is being tracked (or otherwise used as a reference forcomparison to the managed portfolio) is intended to refer to anyportfolio of financial assets or to any financial index, such as the S&P500 or the Dow Jones Industrial Average.

The first section of the following disclosure describes certain metricsfor use in evaluating a portfolio of financial assets, such as stocks orbonds. The second section describes techniques for adjusting a portfolioof financial assets, in order to track the performance of an index, suchas the S&P 500. The third section describes techniques for comparing theperformance of one asset to the performance of another asset.

Asset Portfolio Evaluation.

A main goal of the present intention is to evaluate a portfolio offinancial assets, which may include any or all of stocks, bonds,commodities, shares in indexes and/or other types of funds, derivativeinstruments and cash. Generally speaking, asset portfolio evaluationaccording to the present invention involves the determination and use of“portfolio ETA® values”. Each of these ETA® values measures the tendencyof the aggregate market value (e.g., including paid and/or announceddividends) of the given portfolio to change based on a change in thedata value for a given factor. That is, each ETA® value (η_(i)) isspecific to a given factor (i) that is likely to be correlated with theaggregate market value for the subject portfolio. All of the ETA® valuesfor a particular asset or portfolio sometimes collectively are referredto herein as the ETA® profile for such asset or portfolio. Once the ETA®values have been calculated, they can be aggregated to provide acomposite risk measure or they can be evaluated individually, e.g., bycomparing them to corresponding ETA® values for a second portfolio (oran index) or by comparing them to a threshold.

Thus, in one embodiment of the invention, illustrated in FIG. 1, ETA®values are calculated and then either: (i) compared individually tocorresponding thresholds; or (ii) aggregated to provide an aggregaterisk measure which is then compared to a threshold or to the aggregaterisk measure for another portfolio. Based on such comparisons, a warningindicator may be generated and displayed or some other action (e.g.,buying or selling one or more assets) automatically may be recommendedor initiated.

Referring to FIG. 1, in step 30 a set of factors is identified.Preferably, the factors are chosen as those being likely to becorrelated with an aggregate market value for a subject portfolio. Thepreferred embodiment of the invention utilizes 18 different factors,although any other number instead may be used. Because it is preferableto capture a variety of different types of risk, generally it will bedesirable to utilize a minimum of 5-10 different factors, eachreflecting a different risk factor.

In the preferred embodiments of the invention, the factors include avariety of macroeconomic and/or financial indicators, such as stockindices (e.g., S&P 500, FTSE 100, Tokyo Exchange), commodity indices(e.g., gold price, energy cost), bond indices (e.g., corporate bondyield, short-term government bond yield, intermediate-term governmentbond yield, long-term government bond yield), inflation indicators(e.g., Consumer Price Index), currency exchange rates (e.g.,Dollar/Euro), production indicators (e.g., housing starts), money supply(e.g., monetary base, M1, M2 or M3), corporate cash indicators, salesfigures (e.g., automobiles, new durables), export figures (e.g.,agricultural exports), and unemployment rate. More preferably, thefollowing 18 factors are utilized:

-   -   FTSE (Financial Times Stock Exchange Index) 100    -   AM London Gold Price Index    -   BAA Corporate Bond Yields    -   Consumer Price Index    -   Short-Term (1-year) Government Bond Yield    -   Intermediate-Term (10-year) Government Bond Yield    -   Long-Term (20-year) Government Bond Yield    -   Tokyo Stock Exchange Index    -   Euro/Dollar Exchange Rate    -   Net U.S. Agricultural Exports    -   Total New Housing Starts    -   Monetary Base (Board of Governor's High Powered Money)    -   M2 Money Supply (Board of Governors Money Supply)    -   Corporate Net Cash Flow    -   Unemployment Rate (all workers, age 18-65)    -   Domestic Automobile Sales    -   U.S. Orders for New Durable Goods    -   Energy Cost Index

Such broad-based macroeconomic and financial factors likely will becorrelated with a variety of different types of financial assets andtherefore may be utilized for a variety of different types ofportfolios. In fact, it often will be desirable to use a fairly genericset of factors, so that the factors will not have to be customized toindividual assets or portfolios. Utilizing a standard set of factorsoften will be highly desirable because the resulting ETA® values canthen be used, e.g., for comparison purposes, across a number ofdifferent portfolios. Of course, if factors specifically tailored to thesubject portfolio are desired, such specialized factors also (orinstead) can be selected, e.g., in any of the ways described in the '748and '025 Applications.

In step 32, the ETA® values corresponding to the identified factors arecalculated for a portfolio under consideration. This step first involvesthe selection of a historical observation period for comparing themarket value of the subject portfolio to the data values of theidentified factors. Preferably, this time period is standardized inorder to facilitate comparisons among different portfolios. Morespecifically, in the preferred embodiments of the invention theobservation period is the three years immediately preceding the currentdate (or other base date). In any event, the selection of theobservation period preferably takes into consideration the trade-offbetween a longer period of time, which would provide a larger number ofdata samples, vs. a shorter period of time (i.e., as close as possibleto the current or other base date), which would more closely reflectcurrent conditions.

Once the observation period has been established, data samples arecollected during this observation period for each of the identifiedfactors and for the market value of the portfolio. Such data are thenused to calculate an ETA® value corresponding to each such factor. Thiscan be accomplished in a number of different ways, but preferably isperformed using a linear or non-linear regression of the portfoliomarket value against the identified factors. Alternatively, the ETA®values can be calculated in any other manner, such as by using any ofthe techniques described in the '748 and '025 Applications. Each ETA®value might measure: how the dollar value of the portfolio (or othersubject asset) is expected to change based upon a unit change in thecorresponding factor; what the percentage change in the dollar value ofthe portfolio (or other subject asset) is expected to be based upon aunit change in the corresponding factor; how the dollar value of theportfolio (or other subject asset) is expected to change based upon apercentage change in the corresponding factor; or what the percentagechange in the dollar value of the portfolio (or other subject asset) isexpected to be based upon a percentage change in the correspondingfactor.

In the preferred embodiments of the invention, the statisticalsignificance of each calculated ETA® value also is determined. Theparticular statistical significance measure utilized can be thecorrelation coefficient (e.g., in the event that a regression isutilized to determine the ETA® values) or any similar or other measure.

Preferably, the calculated ETA® values also are displayed in step 32. Asnoted above, each calculated ETA® value indicates a measure of thetendency of the aggregate market value of the subject portfolio tochange based on a change in the data value for the corresponding factor.Thus, each ETA® value typically corresponds to a sensitivity, anelasticity or a similar measure of the subject portfolio in relation tothe corresponding factor. If any particular ETA® value becomes too high,the portfolio may be deemed too risky in that regard. Accordingly, themere display of the ETA® values often can provide a good indication ofthe portfolio's risk profile. This is particularly the case if thefactors are chosen to reflect fairly discrete components of the economythat are largely independent of (or uncorrelated with) each other. TheETA® values may be displayed numerically, graphically or both.Preferably, any display of the ETA® values also includes an indicationas to the statistical significance of each such ETA® value, e.g., bydisplaying the ETA®) values differently depending upon their statisticalsignificances.

Next, in step 34 an aggregate risk measure (ARM) is calculated for theportfolio by aggregating the various ETA® values calculated in step 32above. The risk measure may be determined by simply adding the absolutevalues (or the squares) of all of the calculated ETA® values (or all ofthe statistically significant ETA® values). If the statisticallyinsignificant ETA® values are to be discarded, then it will be necessaryto calculate a measure of the statistical significance of each ETA®value and then discard those ETA® values having a statisticalsignificance value that is below a specified threshold. Thus, forexample, the ARM may be calculated as follows:

$\begin{matrix}{{ARM} = {\sum\limits_{i = 1}^{M}\;{\eta_{i}}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$where

ARM is the aggregate risk measure for the portfolio, and

M is the number of statistically significant ETA® values (e.g., thosehaving a statistical significance higher than a given threshold)

The ARM defined in Equation 1 above sometimes is referred to as theComposite MacroRisk Index (CMRI). It should be understood that the CMRIrepresents only one possible example of an ARM.

Rather than simply discarding the “statistically insignificant” ETA®values, it also is possible to weight each ETA® value by its statisticalsignificance or by a function of its statistical significance. Stillfurther, rather than (or in addition to) performing a summation (or aweighted summation) of a function of the various ETA® values, an averageor a weighted average of the ETA® values may be calculated (e.g., usingthe calculated statistical significances, or a function thereof, as theweights). Thus, for example, the aggregate risk measure instead may becalculated as:

$\begin{matrix}{{ARM} = \frac{\sum\limits_{i = 1}^{N}\;{w_{i}{\eta_{i}}}}{\sum\limits_{i = 1}^{N}\; w_{i}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$where

ARM is the aggregate risk measure for the portfolio,

N is the total number of ETA® values, and

w_(i), is the weight associated with each ETA® value, which may be thestatistical significance of the ETA® value or a function of suchstatistical significance.

Once the foregoing quantities have been calculated, they can be comparedagainst similar quantities for an index 35 and/or evaluated individually41. Often, comparing the subject portfolio to an index 35 will providemore meaningful information. Therefore, this approach is discussedfirst.

As shown in FIG. 1, the initial step 36 in comparing a given portfolioto an index (or other portfolio) 35 is to calculate the ETA® values forthe index. This can be done in the same manner as described in step 32above for calculating the ETA® values for the initial portfolio.Preferably, the same factors are utilized and the data are observed overthe same (or similar) period of time as was used to calculate the ETA®values for the subject portfolio.

It is noted that instead of (or in addition to) displaying the portfolioETA® values in step 32, such ETA® values may be displayed in this step36 together with the ETA® values for the index. One benefit of doing sois that the end user often will be able to more easily compare theportfolio ETA® values with those for an index (or other portfolio) thatthe user may wish to emulate. Once again, it may be preferable tocalculate and display the statistical significances of the ETA® valuesfor the portfolio and for the index, together with the actual ETA®values. One such technique for doing so is to display the subject ETA®values differently depending upon their statistical significances (e.g.,using different colors or different intensities for different levels ofstatistical significance).

Next, in step 38 an aggregate risk measure is generated for the index.Once again, this step preferably is performed in the same manner as thecalculation of the aggregate risk measure for the subject portfolio instep 34. Also, it is noted that steps 36 and 38 frequently can beperformed in advance (e.g., on a periodic basis), with the subjectvalues then simply being retrieved as needed.

In step 40, at least one of the calculated quantities for the subjectportfolio is compared against the corresponding quantity for the index.For example, the aggregate risk measures for the two portfolios may becompared against each other. Alternatively, individual ETA® values forthe portfolio may be compared against the corresponding ETA® values forthe index.

The comparison may take any of a variety of different forms. Forexample, where it is desired to compare single quantities, one may usethe absolute value or the square of the difference between the twocorresponding quantities for the two different portfolios. Thus, withrespect to the aggregate risk measure, one may calculate:Comp.=|ARM_(P)−ARM_(I)| or (ARM_(P)−ARM_(I))²   Equation 3where

Comp. is the comparison measure

ARM_(P) is the aggregate risk measure for the portfolio, and

ARM_(I) is the aggregate risk measure for the index.

As indicated above, typically a difference is calculated between the twoARMs to be compared. However, it also is possible to calculate and thenuse a ratio of such compared quantities. A similar calculation as inEquation 3 may be calculated with respect to each of the individual ETA®values.

Alternatively, as noted above, it is possible to simply display thevalues for the portfolio simultaneously with the corresponding valuesfor the index, thereby allowing the user to visually observe anydifferences. Numeric and/or graphical displays may be utilized for thispurpose.

In the technique described above, certain quantities for the subjectportfolio are compared against corresponding quantities for a referenceportfolio or index (path 35). However, it also is possible to evaluatethe quantities calculated for the subject portfolio in isolation, or incomparison to other information (path 41). Thus, in step 42 each of theindividual ETA® values and/or the ARM for the subject portfolio iscompared against a corresponding threshold.

The comparison of the calculated quantities (e.g., individual ETA®values or the ARM) to a threshold often can provide the basis forautomatically generating a warning or initiating some other action (asdescribed below in connection with step 44). The threshold to which thedesired quantities are compared can be fixed by the user or can bevaried based on other data. For instance, the ARM threshold may be setbased upon historical values of the ARM for a particular index (e.g.,with respect to a stock portfolio, the S&P 500), based upon volatilityin the relevant market (e.g., with respect to a bond portfolio, currentinterest rate fluctuations) or based upon any other information.

In step 44, an action is triggered automatically based upon thecomparison in step 40, in step 42, or both. Thus, for example, if any ofthe calculated quantities exceeds the threshold to which it has beencompared, the system may provide a warning to the end user.Alternatively, any single condition or any desired combination ofconditions may automatically trigger additional processing, such as theautomatic purchasing or selling of assets. Such automatic purchasingand/or selling may be in an attempt to adjust the portfolio as describedin more detail in the section titled “Asset Portfolio Tracking” below.Also, the purchase and/or sale decisions may be implementedautomatically or may be simply suggested to the end user for the enduser to make the ultimate determination.

For the purpose of implementing or recommending appropriate buy/sellorders, a system according to the present invention preferably haswithin its database pre-calculated ETA® values for many if not all ofthe individual assets within the portfolio. These ETA® values can becalculated in the same manner used to calculate the ETA® values for theportfolio as a whole. In fact, the portfolio ETA® values can even begenerated in step 32 above by combining the ETA® values for theindividual assets within the portfolio. In addition, the system'sdatabase preferably includes ETA® values for assets that are notpresently in the portfolio but are considered as potential candidates tobe added to the portfolio. In the preferred embodiments of theinvention, the individual asset ETA® values are updated periodically(e.g., on the same schedule as the ETA® value calculations for theindex). Accordingly, current individual asset ETA® values only need tobe retrieved when needed.

Then, for example, if the system determines that the portfolio hasexcessive risk with respect to one or more factors, some of the assetswithin the portfolio that have the highest risk exposure with respect tothose factors may be sold. Alternatively, assets having high ETA® valueswith respect to those factors, but in the opposite direction as thecorresponding ETA® value for the portfolio as a whole, may be added tothe portfolio. Once again, more detail regarding such portfolioadjustment to obtain an acceptable risk profile is discussed below.

In the embodiment described above, the focus is on the individual ETA®values and on the ARM (which is calculated based on the individual ETA®values). In an alternate embodiment, the individual ETA® values of theportfolio are compared to the corresponding ETA® values for the index.Such a technique is preferred in certain cases, particularly when onewishes to track or emulate the index using a (typically smaller)portfolio of financial assets (and/or assets not contained in theindex).

Thus, referring to FIG. 2, in step 70 a set of factors is identified.Preferably, the factors are chosen as those being likely to becorrelated with an aggregate market value for a subject portfolio and/orwith an aggregate market value for an index to be tracked. The preferredembodiment of the invention utilizes the same 18 factors identifiedabove, although any other factors and/or number of factors may insteadbe used. Once again, because it is preferable to capture a variety ofdifferent types of risk, generally it will be desirable to utilize aminimum of 5-10 different factors.

As in the embodiment described above, the use of broad-basedmacroeconomic and financial factors tends to increase the likelihoodthat such factors will be correlated with a variety of different typesof financial assets and therefore may be utilized for a variety ofdifferent types of portfolios. Once again, however, if factorsspecifically tailored to the subject portfolio are desired, they can beselected, e.g., in any of the ways described in the '748 and '025Applications.

In step 72, the ETA® values corresponding to the identified factors arecalculated for the portfolio under consideration. This step may beperformed, e.g., in any of the ways described above in connection withthe description of step 32. In addition, the calculated ETA® valuespreferably are displayed in this step 72.

In step 74, the ETA® values corresponding to the identified factors areobtained for the index (or other portfolio). Once again, these valuescan be calculated in the same manner as described in step 32 above ormaybe simply retrieved from storage if pre-calculated. Preferably, thesame factors are utilized and the data are observed over the same (orsimilar) period of time as was used in step 72 to calculate the ETA®values for the subject portfolio.

In step 76, ETA® divergence measures are calculated between the ETA®values for the subject portfolio and the ETA® values for the index. Suchdivergent measures sometimes collectively are referred to herein as thedivergent ETA® profile. One technique for calculating such measures isas follows:d _(i)=η_(Pi)−η_(Ii)   Equation 4where

d_(i) is the divergent measure for factor i,

η_(Pi) is the portfolio ETA® value for factor i, and

η_(Ii) is the index ETA® value for factor i.

The foregoing technique simply calculates the difference between the twocorresponding ETA® values. However, the ETA® divergences instead may bedefined to be a function of such difference, such as (i) an exponentialfunction of the difference; (ii) a power of the difference, but with thesign retained; or (iii) for purposes where direction is unimportant, theabsolute value or the square of the difference.

Alternatively, the ETA® divergence measure may be calculated as, or as afunction of, the ratio of the two corresponding ETA® values, e.g.:d _(i) =f(η_(Pi)/η_(Ii))  Equation 5where f(x) may be defined, e.g., to equal x, log(x) or x^(y), in any ofthe foregoing cases with the sign retained or discarded, as appropriate

For purposes of the following discussion, it is assumed that the ETA®divergence measure is calculated as shown in Equation 4. However, any ofthe other ETA®) divergence measures instead may be used.

Once the ETA® divergence measures have been obtained, they may beevaluated directly or may be combined to provide an overall divergence(or tracking error) measure. With regard to the former, in step 77 eachindividual ETA® divergence is compared against a threshold. Thethreshold may be the same across all ETA® divergences or may bedifferent for each. For instance, each such threshold may be a functionof the variance or standard deviation of the ETA® value over time withrespect to the subject index.

As to the latter, in step 78 the individual ETA® divergence measures areaggregated. For example, an aggregate ETA® divergence measure (ortracking error) may be calculated as:

$\begin{matrix}{{TrackingError} = {\eta_{EE} = \sqrt{\frac{\sum\limits_{i = 1}^{M}\; d_{i}^{2}}{M}}}} & {{Equation}\mspace{14mu} 6}\end{matrix}$where

η_(EE) is defined as the ETA® emulation error, and

M is the number of ETA® values that are statistically significant,depending upon the specific embodiment, for the portfolio, for the indexor for both.

In Equation 6 above, all of the statistically significant divergent ETA®measures are combined equally. However, similar to the above-referencedcombination of individual ETA® values, it also is possible to weight theindividual divergent ETA® measures, such as:

$\begin{matrix}{{{TrackingError} = {\sum\limits_{i}\;{w_{i}{d_{i}}}}};} & {{Equation}\mspace{14mu} 7}\end{matrix}$

$\begin{matrix}{{{TrackingError} = {\sum\limits_{i}\;{w_{i}{d_{i}}^{2}}}};{or}} & {{Equation}\mspace{14mu} 8}\end{matrix}$

$\begin{matrix}{{TrackingError} = \sqrt{\frac{\sum\limits_{i = 1}^{N}\;{w_{i}d_{i}^{2}}}{\sum\limits_{i = 1}^{N}\; w_{i}}}} & {{Equation}\mspace{14mu} 9}\end{matrix}$where

w_(i) may be a constant or, e.g., may be a function of the statisticalsignificance of the ETA® value for the portfolio, the ETA® value for theindex, or both, and

in each case, the summation preferably is performed over all divergentETA® measures (corresponding to all of the factors or all of the ETA®values, i.e., without discarding the statistically insignificant values,but instead applying a lower weight to them), although in this case toothe statistically insignificant values may be discarded.

Any of a variety of different techniques for combining the variousdivergent ETA® measures in order to provide a measure of tracking errormay be utilized. Accordingly, the tracking errors defined above shouldbe understood to be merely exemplary.

Next, in step 80 the calculated tracking error is compared against athreshold. Once again, the threshold may be a fixed quantity or insteadmay be a function of one or more of the quantities, such as measurementsof historical variations in the ETA® values.

In step 82, an action is triggered automatically based upon thecomparison in step 77, in step 80 or both. Thus, for example, if any ofthe calculated quantities exceeds the threshold to which it has beencompared, the system may provide a warning to the end user.Alternatively, any single condition or any desired combination ofconditions may automatically trigger additional processing, such as theautomatic purchasing or selling of assets. Once again, such automaticpurchasing and/or selling may be in an attempt to adjust the portfolioas described in more detail in the section titled “Asset PortfolioTracking” below. Also, the purchase and/or sale decisions may beimplemented automatically or may be simply suggested to the end user forthe end user to make the ultimate determination. As in the previousembodiment, for the purpose of implementing or recommending appropriatebuy/sell orders, a system according to the present invention preferablyhas within its database pre-calculated ETA® values for many if not allof the individual assets within the portfolio.

Asset Portfolio Tracking

The ETA® values and ETA® profiles described above can be used tofacilitate tracking of an index or other portfolio. For example, amanager of a relatively small fund may wish to track a much largerindex, such as the S&P 500. Even where a fairly large fund is beingmanaged, it often will be the case that relatively small transactionsneed to be made (e.g., to invest additional funds or to sell off someassets to obtain cash). Also, a decision might be made to alter theinvestment strategy for an existing portfolio so that the portfoliobegins to track a specified index. The following techniques generallycan permit systematic identification of particular assets to buy orsell, often permitting good tracking of an index in such cases withoutthe necessity of buying or selling proportionate holdings for the entireindex.

One of the simplest techniques according to the present invention is toobtain the divergent ETA® profile between the managed portfolio and thetracked index, identify the individual asset (e.g., stocks) that has anETA® profile as close as possible to such divergent ETA® profile (or tothe negative of the divergent ETA® profile), buy or sell such asset asappropriate in order to reduce the divergent ETA® profile as much aspossible, and then repeat the process. In one embodiment of thistechnique, it is assumed that modifications need to be made to aportfolio being managed in order to invest additional funds or toliquidate some of the assets in the portfolio to satisfy cash needs(e.g., to distribute to investors who have sold their shares in thefund).

Referring to FIG. 3, in step 102 the ETA® values are obtained for theindex to be tracked. In the preferred embodiments of the invention,these ETA® values previously have been calculated (e.g., using any ofthe techniques described above) and are available to be retrieved. Morepreferably, the ETA® profile for the index is calculated on a periodicbasis (e.g., daily or weekly), and the most current values can beretrieved when needed. Of course, tracking of the ETA® profile for theindex implies a previous selection of factors to which the ETA® valuescorrespond. Those factors may be selected in accordance with thecriteria set forth above and, once selected, generally will continue tobe used over a long period of time. However, it is possible to add newfactors, delete existing factors or replace factors over time aseconomic conditions change (new dependencies arise or existingdependencies become obsolete), new information becomes available and/oras the relationships between the individual factors change over time(e.g., where two of the factors being utilized become increasinglycorrelated with each other).

In step 104, ETA® values are obtained for the portfolio being managed.These values also may be calculated using any of the techniquesdescribed above. They may be recalculated as needed (e.g., in order toobtain the most current information), but ordinarily previously willhave been calculated, e.g., in the other steps of this method) andtherefore will be available to be retrieved.

In step 106, the ETA® divergent profile is calculated between theportfolio being managed and the index being tracked. Once again, thesequantities may be calculated using any of the techniques describedabove.

In step 108, the ETA® divergences are aggregated in order to determine ameasure of the tracking error. Once again, this measure may becalculated using any of the techniques described above.

In step 112, the best asset to buy or sell is identified. Typically, ifcash needs to be put into the managed portfolio then the process onlywill look at purchasing additional assets, and if cash needs to be takenout of the portfolio then the process will only look at selling assets.However, in either such case the opposite transaction may be performedin order to provide additional flexibility in reaching the ultimate goalof more closely tracking the subject index, provided that subsequentoffsetting transactions are identified so that the total amount of cashat the end of the process satisfies the applicable constraints.

Preferably, step 112 selects the asset that has an ETA® portfolio thatis as close as possible to the divergent ETA® profile (for assets to besold) or has an ETA® profile that is as close as possible to thenegative of the divergent ETA® profile (for assets to be acquired). Asindicated above, it often is desirable (but not necessary) to look onlyat possible purchases or only at possible sales.

In addition, it might be desirable to consider other criteria as well.For example, one might wish to constrain the search for possible assetsto a limited subset that is manually selected or that is automaticallyselected to achieve some other goal. One such goal might be to have themanaged portfolio resemble as closely as possible the makeup of theindex being tracked, so that a casual observer will not notice too manydifferences between the managed portfolio and the tracked index. It isnoted that if the ETA® factors are selected appropriately, such aconsideration likely would be primarily for purposes of appearance.However, such appearances might matter to a potential investor,particularly if the investor is not aware of the present ETA® trackingtechnique.

Thus, the buy list or the sell list, as appropriate, may be generated inany of a variety of different ways and based upon any of a variety ofdifferent considerations. Of course, the simplest technique is to useall of the assets in the portfolio as the sell list and to use all ofthe assets in the index (although any other relevant universe may beused) as the buy list.

In any event, once the appropriate buy list and/or sell list has beenestablished, the specific asset may be selected from the list. For thispurpose, it is preferable to examine the ETA® profiles for all of theassets under consideration. With this information, an appropriate assetmay be identified, e.g., by finding the asset in the subject list(s)that satisfies the following:

$\begin{matrix}{{\max\limits_{a}( {\sum\limits_{i}\;{d_{i}f_{a}{\hat{\eta}}_{ai}}} )},} & {{Equation}\mspace{14mu} 10}\end{matrix}$where

is the maximum over all assets α;

d_(i); is the divergent measure between the ETA® values for the managedportfolio and the tracked index with respect to factor i;

f_(α)is +1 if the asset is to be sold and −1 if the asset is to bepurchased; and

{circumflex over (η)}_(αi) is the ETA® value of asset α with respect tofactor i, normalized so that the ETA® profile for all assets have thesame “magnitude”, e.g.:

${{\hat{\overset{-}{\eta}}}_{a} = \frac{{\overset{\_}{\eta}}_{a}}{\overset{\_}{\eta}}},$where

η _(α)is a vector of the ETA® profile for asset α;

∥ η _(α)∥ is the magnitude of the vector; and

{circumflex over (η)} _(α) is the normalized vector.

Alternatively, any corresponding measurement may be utilized for findingthe asset (from a given list or set) whose ETA® profile most closelycorresponds to the divergent ETA® profile. For example, the effect of apurchase or sale (as applicable) of a small incremental amount of eachpotential asset/transaction on the tracking error may be examined, andthe asset/transaction with the greatest reduction selected. In anyevent, by the conclusion of this step 112, both an asset and a type oftransaction (i.e., purchase or sale) will have been identified.

In step 114, the quantity of the purchase or sale is determined. Thisstep may be performed in a variety of different ways. In the preferredembodiments of the invention, the goal is to minimize the aggregatetracking error as much as possible, subject to any other constraints,such as: the total maximum amount of cash that can be put into orwithdrawn from the managed portfolio; or the maximum amount of theparticular asset that can be purchased or sold, as the case may be(which amount may be specified by the user or may be set based uponother considerations, e.g., a rule against short-selling or a generalrule that no single asset may comprise more than x percent of the totalportfolio).

Depending upon how the ETA® values and the corresponding ETA®discrepancies are defined, it may be possible to calculate a closed formsolution to determine the transaction volume that will minimize thetracking error. For example, such a solution may be possible where theETA® profile for a given portfolio is simply the weighted sum of theETA® profiles for the assets within the portfolio. It is noted that anysuch solution should account for the fact that each transaction resultsnot only in the acquisition or divestiture of a quantity of an asset,but also in a corresponding divestiture or acquisition of cash (which,of course, has an ETA® profile of all zeros). Once the optimal quantityis determined in accordance with such a closed form solution, it may bemodified as necessary in accordance with any of the aforementionedconstraints to provide the output quantity.

However, in certain cases it will not be possible to determine aclosed-form solution to the problem. In such cases, the optimalquantities (or the constraint-modified optimal quantities) may bedetermined using any of a variety of numerical searching techniques,including incremental analysis, interpolation, extrapolation or anycombination of the foregoing. In most of such techniques, anyuser-specified or other constraints can be built into the process (i.e.,by limiting the range of potential transaction quantities that are to besearched). As a result, it generally will not be necessary to modify theresulting quantity.

In step 116, any necessary modifications to the specified constraintsare made. For instance, if one of the constraints previously limitedadditional purchases of asset x to 10,000 shares, but only 6,000 shareswere required to be purchased when the optimal quantity was reached,then the constraint should be modified so that no more than 4,000additional shares of asset x may be purchased. Similarly, if theforegoing purchase requires $180,000, then that amount should bededucted from the required additional quantity of cash to invest intothe managed portfolio.

In step 118, a determination is made as to whether the required cashcriterion has been satisfied. As noted above, the usual motivation forexecuting the present process is to either put additional cash into themanaged portfolio or take cash out of the portfolio. Thus, in this stepit is determined whether there have been enough net purchases or salesto satisfy the specified criterion. If so, then processing proceeds tostep 119.

In step 119, the identified transactions either are recommended (e.g.,in the event that the foregoing process steps are executed by a computerand a human being is required to make the final transaction decisions)or are executed (e.g., automatically by a computer or by the same personwho performed the foregoing process steps).

Alternatively, if a negative determination was made in step 118, thenprocessing proceeds to step 104. In step 104, a new ETA® profile iscalculated for the portfolio (assuming execution of the transaction thatwas just identified). It is noted that this calculation (together withany or all of the calculations to be made in the following steps 106 and108) often will already have been performed in connection with thepreviously discussed steps for identifying the transaction.

As result of the foregoing process, a combination of transactions isidentified. It should be apparent that the goal of each transaction inthe foregoing process is to minimize the tracking error. Eventually,enough transactions are performed that the required cash inflow oroutflow is accommodated.

The foregoing process is flexible enough to accommodate a number ofvariations. For example, a user may manually specify a certain number oftransactions and then cause the foregoing process to be performed inorder to specify the remainder of the transactions. In such a case, theuser-specified transactions preferably are performed first, therebyallowing the foregoing process the maximum flexibility in realigning theETA® profiles of the managed portfolio and the tracked index.

As already noted above, a variety of different transaction preferencesand constraints also may be accommodated in the foregoing process. Theseinclude constraints regarding the final cash position of the portfolio,maximum quantities of particular assets to be included within theportfolio, and general preferences, such as a preference that the finalportfolio have approximately the same proportionate composition as thetracked index.

In the process described above, a direct sequence of transactions isidentified.. While such a technique generally will be adequate, in manycases it will not find the optimal solution. For example, if only asingle transaction is required the process described above typicallywill provide a very good result. However, if two transactions ultimatelyare required to satisfy the cash-flow criterion, a process in which eachstep is optimized in isolation might result in a non-optimalcombination. This can be seen graphically with reference to FIGS. 4A-C.

Specifically, FIGS. 4A-C illustrate the problem of moving from an ETA®profile for the managed portfolio (illustrated as starting point 130) toan ETA® profile for the index being tracked (illustrated as point 131)in a two-dimensional space (corresponding to two ETA® factors). In eachof FIGS. 4A-C, only three assets are available for purchase or sale,represented by the three directional vectors 132-134. It is furtherassumed that the negatives of vectors 132-134 are not available (i.e.,only one type of transaction, purchase or sale, is available). Theproblem then is how the three assets (or correspondingly the threedirectional vectors) can be utilized to move the ETA® profile for themanaged portfolio as close as possible to the tracked ETA® profile 131.

FIG. 4A illustrates the three optimal quantities for each asset 132-134.As is readily apparent, the method described above would result in atransaction involving asset 133, in the quantity illustrated, for thefirst transaction. That is, such a transaction would move the managedportfolio ETA® profile closest to the desired ETA® profile. This clearlyis the optimal solution if only a single transaction is required.

On the other hand, the situation changes if another transaction isrequired. For example, if assets are being purchased and a singletransaction does not result in a sufficient amount of cash beingtransferred into the managed portfolio, then the method described abovewould require a second transaction.

The effect of such a subsequent transaction is illustrated in FIG. 4B.At this point, after purchasing the quantity of asset 133 shown in FIG.4A, the optimal transaction would be to purchase a quantity of asset134. More specifically, the ideal transaction would be to purchase aquantity of asset 134 that would result in vector 136. Such atransaction clearly would move the ETA® profile of the managed portfoliocloser to the ETA® profile 131 of the tracked index.

However, if it were known from the outset that two transactions wererequired, a different course of action would have been optimal. Forinstance, still referring to FIG. 4A, the first transaction could havebeen the purchase of asset 132 in the quantity indicated by that vector.Then, the optimal second transaction would have been an appropriatequantity of asset 134 (in the quantity indicated vector 135). Thistwo-transaction combination would have resulted in an end state that wasexactly as desired (i.e., an ETA® profile that is exactly equal toprofile 131), which is a clear improvement over the result that wouldhave been achieved with the method described above. An equally goodresult, also shown in FIG. 4A, would have been achieved by firstselecting a transaction represented by vector 134 and then selecting atransaction represented by vector 137.

FIG. 4C illustrates yet another way that the optimal result could havebeen achieved. With this result, the first transaction still involves aquantity of asset 133 (represented by vector 138), but one in which thequantity is smaller than what is illustrated in FIGS. 4A-B. If thequantity were in fact restricted as illustrated in FIG. 4C, then thenext optimal step (even in accordance with the foregoing method) woulddictate a quantity of asset 134 (as represented by vector 139). Onceagain, the result would be to end up at exactly the desired ETA® profile131.

Both of the improved solutions illustrated in FIG. 4B and FIG. 4Ctypically will require some amount of looking ahead, which is notaccommodated by the method of FIG. 3. The question then it is how toefficiently implement such looking ahead. It is of course possible toperform an exhaustive search of nearly all possible combinations oftransactions. However, the amount of time and/or resources required toperform such a search would be impractical. However, near-optimalresults often can be obtained using the techniques described hereinand/or other sub-optimal techniques.

For example, in the second embodiment described below in connection withFIGS. 5-7, a tree-searching process is performed. In the thirdembodiment described below in connection with FIG. 8, subsets of theavailable assets that are likely to lead to good results arepre-generated. FIG. 9 illustrates a portfolio adjustment technique thatis similar to the technique shown in FIG. 5, but that may be utilizedwhen required cash flow is not the driving factor.

In addition, the use of look-ahead processing with regard to thequantity of a particular asset to purchase or sell can be incorporatedinto step 114, described above, in order to provide a more optimalembodiment. For instance, rather than simply selecting the quantity thatmoves the ETA® profile for the managed portfolio closest to the ETA®profile for the tracked index, a modified quantity may be selected inview of the ETA® profiles for the other potential assets. In thisregard, with reference to FIGS. 4A-C, an optimal quantity irrespectiveof any subsequent transaction may be identified (as in FIG. 4A). Then,an optimal quantity assuming that the next transaction involves eachother potential asset may be identified.

Such a technique is illustrated by referring back to FIGS. 4A-C. Whenviewed in isolation, the quantity of asset 133 is as shown in FIGS.4A-B. When assuming that the next transaction would involve a scaledversion of the vector 134, the quantity for the initial transactionshown in FIG. 4C would result. When assuming that the next transactionwould involve a scaled version of the vector 132, the quantity for theinitial transaction shown in FIG. 4A again would result, because nosubsequent transaction involving asset 132 would result in a better ETA®profile. Thus, the optimal transaction would include vectors 138 and139, as shown in FIG. 4C.

It is noted that if both purchases and sales of each asset arepermitted, a scaled version of vector 132 would be possible for thesecond transaction. In that case, the quantity 140 (shown in FIG. 4D)preferably would be determined for the asset 133, and then the quantity141 (also shown in FIG. 4D), which is in the reverse direction andtherefore would correspond to the opposite transaction, would beselected for asset 132.

It is further noted that the examples illustrated in FIGS. 4A-D are muchsimpler than the problems that would be encountered in a real-worldsituation, given that the cited example involves only two ETA® factorsand three potential assets, as compared, e.g., to 18 ETA® factors andhundreds of potential assets. In addition, it typically will not be thecase that simple vector addition can be utilized to determine the effectof any given transaction on the ETA® profile for the managed portfolio.At the very least, any real transaction will generate or absorb cash,which will have the effect of modifying the ETA® profile that otherwisewould result. Nevertheless, such additional operations arestraightforward to implement and, even if they cannot be easilyrepresented in a closed form, can be readily simulated on a computer. Asimilar comment applies to other references herein in which ETA®profiles are represented as vectors and/or in which purchases or salesof assets are represented as simple vector operations.

As noted above, FIG. 5 illustrates a tree-searching process that oftencan provide near-optimal results, by providing a degree of lookingahead. Referring to FIG. 5, in step 102 (described above) the ETA®profile is obtained for the tracked index.

Next, in step 150 the ETA® profile is obtained for the managedportfolio. The first iteration of this step is identical to step 104(described above in connection with the discussion of FIG. 3). Insubsequent iterations, multiple states (each corresponding to adifferent transaction sequence) typically will be considered, and anETA® profile is obtained for the portfolio with respect to each suchstate (or transaction sequence).

In step 152, an ETA® divergent profile is generated for each state. Thisstep is similar to step 106, except that after the first iteration theregenerally will be multiple states, rather than just one, for which anETA® divergent profile will need to be calculated.

In step 154, a tracking error is calculated for each state. This step issimilar to step 108, except that after the first iteration theregenerally will be multiple states, rather than just one, for which atracking error will need to be calculated.

In step 156, a new set of states is generated for each existing state.This step generally involves, for each current state, generating a setof possible transactions that are likely to be optimal or near-optimalgiven such state. The resulting multiplicity of states then can bepruned to eliminate those which do not appear to correspond to optimaltransaction sequences. Step 156 is discussed in more detail below inconnection with FIGS. 6 and 7.

In step 158, a determination is made as to whether or not the specifiedcash-flow criterion has been satisfied. This step is similar to step118, except that after the first iteration there generally will bemultiple states to consider in this step. Because each state reflects adifferent transaction sequence history, each such state typically willresult in a different net cash flow. Preferably, an affirmativedetermination is made in this step 158 only if the cash criterion hasbeen satisfied for all existing current states. If not, then processingreturns to step 150 to obtain the ETA® profile for each existing state.As with the process according to FIG. 3, many of such ETA® profilesalready will have been calculated (in connection with the performance ofstep 156) and therefore need only be retrieved.

On the other hand, if the cash criterion has been satisfied for allexisting final states, then processing proceeds to step 160 in which thebest state (and, correspondingly, the best sequence of transactions) isselected. Preferably, this determination is made by calculating (orobtaining, if previously calculated) a tracking error for each suchfinal state. The best state can then be selected as the one having thesmallest tracking error.

Alternatively, the tracking error may be utilized in combination withany other user-specified criteria. For example, the user might set acriterion that attempts to match the proportionate makeup of the managedportfolio to the proportionate makeup of the index. In the event thatmultiple criteria are utilized, any desired weights may be specifiedwith respect to each such criterion.

In any event, in step 161 the identified transactions either arerecommended (e.g., in the event that the foregoing process steps areexecuted by a computer and a human being is required to make the finaltransaction decisions) or are executed (e.g., automatically by acomputer or by the same person who performed the foregoing processsteps).

FIG. 6 illustrates a process for generating a new set of states from theexisting set of states (i.e., step 156 in FIG. 5), according to thepresent invention. Initially, in step 180 the buy/sell prospects for thecurrent state are identified. In this regard, the input to the processillustrated in FIG. 6 might consist of a single state (e.g., in thefirst iteration of the process shown in FIG. 5), but more typically willconsist of multiple different states, with a different state beingprocessed in each iteration of loop 181.

Step 180 preferably is similar to the step 112 (shown in FIG. 3). Forexample, the same considerations apply in determining the overall buyand/or sell lists. However, rather than finding a single best candidateasset to buy or sell, in step 180 multiple assets may be identified. Inthis regard, the precise number of assets identified may be fixed foreach iteration of step 180 (i.e., always selecting the best N assets) ormay be varied from iteration to iteration. For example, in oneembodiment the process selects any assets having a normalized ETA®profile whose inner product with the normalized divergent ETA® profileexceeds a specified threshold. Alternatively, rather than using a fixedthreshold, the threshold may be varied from iteration to iteration basedupon any natural clustering of such inner products across all potentialassets.

In step 182, the optimal quantity is determined for each buy-sellprospect. This step is similar to step 114 discussed above (and shown inFIG. 3) and may be implemented with or without look-ahead processing, asalso discussed above.

In step 184, a determination is made as to whether the last of thecurrent states has been processed. If not, then the next of the currentstates is selected in step 185 and processing returns to step 180 torepeat the process for this next state. Once all of the current stateshave been processed, processing proceeds to step 186.

In step 186, the newly generated states are pruned. In this regard,multiple new states (each corresponding to a different next-subsequenttransaction) typically will have been generated for each of thepreviously existing states. Accordingly, in order to avoid anexponential growth in the number of states that must be processed, itgenerally will be desirable to eliminate some of the newly generatedstates. This can be accomplished, e.g., by calculating a tracking errorfor each new state and eliminating all states except those having thelowest tracking errors. Alternatively, if a look-ahead processing isimplemented in either or both of steps 180 and 182, the likelylook-ahead tracking error (i.e., after taking into account anticipatedsubsequent transactions) instead may be used.

The precise number of states to retain may be fixed for each iterationof step 186 (i.e., always selecting the best M states) or may be variedfrom iteration to iteration. For example, in one embodiment the processselects any states having a tracking error that is lower than aspecified threshold. Alternatively, rather than using a fixed threshold,the threshold may be varied from iteration to iteration based upon anynatural clustering of the tracking errors over all of the states.

In step 188, the constraints pertaining to the newly generated statesare adjusted from the corresponding constraints for the states fromwhich such newly generated states have been generated. For example, ifthe parent state required an additional $100,000 to be invested into themanaged portfolio and the transaction that resulted in the new staterequired a $70,000 investment, then the constraint would be modified torequire an additional $30,000 to be invested into the managed portfolio.Similarly, if the parent state limited acquisitions of the asset to3,000 shares and 2,000 shares of the asset were purchased to generatethe new state, then the criterion would be modified to permit anadditional acquisition of no more than 1,000 shares of the asset.

An illustration of the foregoing tree-searching technique, with pruning,is illustrated in FIG. 7. In the example shown in FIG. 7, four newstates are generated from each existing state (i.e., starting from eachexisting state, the four “best” transactions to perform next areidentified). Then, after an entire level of new states has beengenerated, those states are pruned so as to retain only the four beststates.

The initial state 220 represents the ETA® profile for the managedportfolio prior to any modifications. From that state, the four besttransactions are identified in step 156, which identification may or maynot involve any forward looking. The result is four new states 222. Eachof these new states 222 then is separately evaluated, and the four besttransactions are identified for each such state 222, in the nextiteration of step 156, resulting in a total of 16 new states. However,in this second iteration of step 156 pruning step 186 is performed, sothat the four best states 224 of the existing 16 are identified, andonly these four states 224 are processed further. Subsequently, four newstates are generated from each state 224, in the manner described above,resulting again in a total of 16 states. From these new 16 states, onceagain only the four best states 226 are selected for further processing.Eventually, each path will terminate when the cash-flow criteria hasbeen satisfied. Then, the best remaining state is selected and thecorresponding combination of transactions (i.e., defined by the pathfrom the initial state 220 to the best final state) is identified. Inthis way, irrespective of how many transactions ultimately are required,no more than 16 states need to be evaluated at any given time.

The techniques described above often can provide good results,particularly where the transaction volume necessary to achieve thespecified cash-flow criterion is approximately the same as or smallerthan the transaction volume necessary to move the ETA® profile for themanaged portfolio from its current state to the ETA® profile for thetracked index. This generally will be the case where the required netcash flow into or out of the portfolio is relatively small, or wherefactors other than cash-flow needs are driving the portfolio adjustment(e.g., in response to a change in investment strategy so as to begintracking a subject index, as described in more detail below inconnection with FIG. 9).

However, where the transaction volume in connection with the cash-flowcriterion is significantly larger than is necessary to align the twoETA® profiles (i.e., “excess cash-flow criterion”), the foregoingtechniques can result in a large number of small transactions that movethe ETA® profile for the managed portfolio within a small region aroundthe vicinity of the ETA® profile for the tracked index. Often, therecommended transaction combination will not be efficient, involving anunduly large number of transactions, and the computation of therecommended transaction combination frequently also will be inefficientin terms of computer processing resources.

FIG. 8 is a flow diagram illustrating a technique for tracking an indexor other portfolio according to a third representative of the embodimentof the present invention. This technique also can provide a more optimalsolution by looking ahead. However, here such looking ahead is done in asomewhat different manner that often can help address theexcess-cash-flow-criterion problem. Basically, the concept in thepresent technique is to first identify multiple potential subsets of theavailable assets, with each such subset having an apparent highlikelihood of being capable of being combined in a manner so as toachieve the desired outcome. Then, each such subset can be separatelyanalyzed to identify an optimal combination of the assets in it.

More specifically, in step 250 a plurality of subsets of assets areidentified, with each subset preferably being significantly smaller thanthe total number of assets that is available for executing transactions.In the preferred-embodiments of the invention, the goal of this step 250is to find a small number of assets whose ETA® profiles appear to becapable of being combined in order to achieve a combined ETA® profilethat is as close as possible to all zeros (or to the divergent ETA®profile for the managed portfolio). In the preceding sentence, the word“small” generally will be defined relative to the cash-flow criterion(or to the excess cash-flow criterion). Once the desired number (orrange of numbers) of assets has been identified, the asset subsets maybe identified using any of a variety of different techniques, includingneural network techniques, linear or other mathematical programmingtechniques, other types of tree-searching techniques, clusteringtechniques, or any combination of the foregoing. Often, in addition toidentifying individual subsets, a byproduct of this step 250 (generatedwhen determining the fitness of each potential subset) will be toidentify at least a rough proportionate combination of the assets ineach subset that is likely to achieve a near-zero combination ETA®profile.

In step 252, an optimal combination of the assets in the current subsetis identified. Preferably, this step is performed by starting with therough proportionate combination identified in step 250 (scaled, ifnecessary, to achieve the allotted cash-flow criterion) and modifyingthe proportionate amounts to optimize the resulting combination ETA®profile. This can be accomplished in any of a variety of different ways,such as by systematically or randomly incrementally modifying theproportionate quantities of each asset using a tree-searching technique,and then using pruning to eliminate the obviously inferior paths.

In step 254, the ETA® profile for the managed portfolio and then thedivergent ETA® profile and tracking error (from the tracked index) arere-calculated for the current subset, on the assumption that thetransactions identified in step 252 will be performed.

In step 256, a determination is made as to whether or not the currentsubset is the last subset identified. If not, then the next subset isselected in step 257 and processing returns to step 252 to beginprocessing that subset. Otherwise, processing proceeds to step 258.

In step 258, the subset (and its corresponding optimal combination ofassets therein) that results in the optimal end state (e.g., closest toa combination ETA® profile of all zeros or the negative of the divergentETA® profile) is identified.

Finally, in step 260 the identified transactions either are recommended(e.g., in the event that the foregoing process steps are executed by acomputer and a human being is required to make the final transactiondecisions) or are executed (e.g., automatically by a computer or by thesame person who performed the foregoing process steps).

The foregoing technique can be particularly well-suited to situationswhere the divergent ETA® profile is small relative to the cash-flowcriteria or, alternatively, where there is a significant amount ofexcess cash-flow criterion. It is noted that the foregoing technique maybe utilized independently or may be combined with any of the othertechniques described above. For instance, 75-90 percent (or a portionthat is based on the magnitude of the divergent ETA® profile) of thecash-flow criterion may be assigned to the technique of FIG. 8. Then,after the process of FIG. 8 has been completed, the balance of thecash-flow criterion, together with the portfolio ETA® profile and anyother modified criteria resulting from the performance of the methodshown in FIG. 8 may be input into any of the other techniques describedabove.

In this way, the technique of FIG. 8 first can be used to absorb most ifnot all of the excess cash-flow criterion (possibly with someimprovement in the divergent ETA® profile, if that is the target of theprocess according to FIG. 8) and then any of the other techniquesdescribed above may be utilized to fine tune the ETA® profile for themanaged portfolio in order to bring it more in line with the ETA®profile for the tracked index. As noted above, the allocation of thecash-flow criterion may be made dynamically. For example, when a certainamount of the cash-flow criterion has been utilized and the remainingcash-flow criterion is believed to be sufficient to move the resultingETA® profile for the managed portfolio close to the ETA® profile for thetracked index, the technique of FIG. 8 may be terminated and any of theother techniques described above initiated.

Also, it should be noted that the process according to FIG. 8 may beutilized in creating a portfolio to track the performance of an index.Such a technique may be especially useful where the portfolio isintended to include a much smaller number of assets than are encompassedby the index.

FIG. 9 illustrates a technique which is similar to the technique shownin FIG. 5, but which can be used for portfolio adjustment irrespectiveof any immediate cash-flow needs. For example, the technique of FIG. 9might be utilized when external factors have caused the ETA® profile forthe tracked index to change. Probably the most common of such situationsis when the composition of the tracked index changes. Another situationmight be where the ETA® profiles for the managed portfolio and thetracked index drift apart based upon changes over time in the ETA®profiles for the individual assets. Yet another situation might be wherethe proportionate makeup of the tracked index effectively changes overtime. With regard to this situation, for example, a company havingdisproportionate increases in its market value might have acorrespondingly increasing impact on the ETA® profile for the trackedindex, depending upon the method by which the return for the trackedindex is calculated. Finally, a decision might be made that an existingportfolio should begin to track a particular index, requiring purchasesand/or sales of assets in order to bring the portfolio in line with theETA® profile of the index. In any of the foregoing situations, as wellas a variety of others, such changes, if not sufficiently addressed bycash-flow-based modifications described above, might require the managedportfolio to be adjusted in order to more closely track the desiredindex.

Preferably, the goal of the technique illustrated in FIG. 9 is todecrease the tracking error to a level below a specified threshold. Inthe preferred implementation of this method, the user specifies anacceptable range for the total net amount of cash that is to be heldwithin the portfolio upon completion of the present adjustment. Unlessotherwise specified by the user, this technique preferably allows forthe sale of any asset within the portfolio or the purchase of any asseton an approved buy list (e.g., any asset in the tracked index).

As will be readily appreciated, other than some differences in thespecified cash-on-hand and other criteria, this technique can be nearlyidentical to the technique described above in connection with FIG. 5. Infact, other than taking into account such different criteria, each ofsteps 102, 150, 152, 154, 156 and 161 in the method of FIG. 9 isidentical to the correspondingly numbered step in the method of FIG. 5.

In step 285, in addition to checking any required net total cashcriterion and any other specified criteria (as in step 158, shown inFIG. 5), a determination also is made as to whether or not the trackingerror has been reduced below a specified threshold. If all of thecriteria have not been satisfied, then processing proceeds to step 156in order to generate a new set of states to be processed. Otherwise,processing proceeds to step 289.

In step 289, the state that satisfied the criteria set forth in step 285is selected. If multiple states satisfied such criteria, then the beststate (e.g., the one that results in the smallest tracking error) isselected.

In a similar manner, it is straightforward to modify the processillustrated in FIG. 8 to permit portfolio adjustment based uponconsiderations other than cash-flow needs.

Prior to execution of any of the tracking techniques described above, itis preferable to perform a step of calculating the effects of anyuser-designated transactions, both on the ETA® profile for the managedportfolio and on the specified constraints. The resulting state(together with the corresponding constraints) then is used as the inputto be selected technique. Ultimately, if it is determined that anacceptable solution cannot be achieved if all of the user-designatedtransactions are performed, a message to that effect may be displayed tothe user and/or the user-designated transactions may be automaticallymodified to the extent necessary to achieve an acceptable trackingerror. Moreover, where the user specifies a set of assets, e.g., to bepurchased, any of the techniques described above may be utilized toidentify the optimal combination of such assets to purchase.

In the preferred implementation of each of the foregoing methods, theuser specifies an acceptable range for the total net amount of cash thatis to be held within the portfolio upon completion of the presentadjustment. The total cash within the portfolio may vary outside of thisrange at certain points within the execution of any such method,provided that appropriate transactions subsequently are scheduled tobring the total portfolio cash within the specified range.

Potential-Based Asset Comparison

FIG. 10 illustrates a flow diagram showing a technique according to thepresent invention for assessing the performance of a portfolio incomparison to the performance of an index. Initially, in step 320factors that tend to influence, or that otherwise are related to, themarket value of an asset under consideration are identified. Preferably,a minimum of 5-10 such factors are used and, more preferably, the 18factors listed above are utilized. However, it is also possible totailor the factors to the specific asset under consideration, e.g.,using any of the techniques described in the '748 and '025 Applications.

In step 322, a model is produced that relates the market value of thesubject asset to the historical data values for the identified factors.In the preferred embodiment of the invention, this step is performedusing a linear or nonlinear multiple regression technique. However, anyof the other techniques described in the '748 and '025 Applicationsinstead may be used. Depending upon the modeling process, the resultingmodel may be expressed as an equation (e.g., for regression techniques)or provided as a computer model (e.g., for models generated usingneural-network techniques) without any identified mathematical form.

The generation of a model in this step 322 typically will require thedesignation of a period of time in which historical data values areobserved. Preferably, this period of time is designated to be the threeyears immediately preceding either the current (or other base) date orthe date that is k prior to the current (or other base) date, wherepreferably k=3 months. However, the observation period instead may beselected using any of the techniques described in the '748 and '025Applications.

In step 324, a price (or market value) estimate is generated using thederived model together with observed data values for the factors. In thepreferred embodiments of the invention, current values (or values as ofthe other base date) are utilized for the factors in this step 324.

Next, in step 328 the market value estimated in step 324 is comparedagainst a market value for the asset that actually has been observed.More specifically, in the preferred embodiments of the invention acomparison measurement between these two quantities is generated. Suchcomparison measurement may be specified in any of a variety of differentways, but preferably is specified in accordance with one of thefollowing formulas:

$\begin{matrix}{{{PotentialIndex}(1)} = \frac{{Model}(1)}{{Actual}( {{base} - k} )}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

$\begin{matrix}{{{PotentialIndex}(2)} = \frac{{{Model}(1)} - {{Actual}({base})}}{{Actual}( {{base} - k} )}} & {{Equation}\mspace{14mu} 12}\end{matrix}$

$\begin{matrix}{{RelativeValueIndex} = \frac{{Model}(2)}{{Actual}({base})}} & {{Equation}\mspace{14mu} 13}\end{matrix}$where

Model(1) is a market-value estimate that has been generated using amodel having an observation period that ends k (e.g., 3 months) prior tothe current (or other base) date and using data values for the factorsas of the current (or other base) date;

Model(2) is a market-value estimate that has been generated using amodel having an observation period that ends at the current (or otherbase) date and using data values for the factors as of the current (orother base) date;

Actual(base) is the actual market value of the asset at the current (orother base) date; and

Actual(base−k) is the actual market value of the asset k (e.g., 3months) prior to the current (or other base) date.

In step 330, the comparison measurement for the current asset(calculated in step 328) is compared against the comparison measurementfor a second asset (e.g., an index or other portfolio), which secondasset may be considered to be a benchmark. The comparison measurementfor the benchmark may be determined by repeating steps 322, 324 and 328above for such second asset. Preferably, the benchmark is an index andthe first asset is a portfolio that attempts to emulate the index. Thecomparison may be performed by simply displaying the comparisonmeasurements for each of the assets. Alternatively, a secondarycomparison measurement may be generated, e.g., using the differencebetween the two comparison measurements or the ratio of one comparisonmeasurement to the other. Such a secondary comparison measurement can beviewed as an intermediate-term estimate of the portfolio alpha withrespect to the benchmark, and is particularly useful where furtheranalysis is desired.

In step 332, assets are purchased and/or sold or recommendations aremade to purchase and/or sell assets based on the comparison made in step330. For example, in step 330 the comparison measurement for thebenchmark may be subtracted from the comparison measurement for thesubject asset. A negative value from such a calculation might suggestthat the portfolio is overvalued as compared to the benchmark. As aresult, selling shares in the subject portfolio might be indicated.Alternatively, a positive value might indicate that it is wise topurchase shares in the subject portfolio. It is noted that thet-statistic provides a measure of the statistical significance of thesecondary comparison measure (or alpha estimate). Such statisticalsignificance should of course be considered when determining whether theresults are sufficiently meaningful to form the basis for anytransactional decisions.

A variety of other measures also may be calculated for an asset. Forexample, one may define the Z-score of the current value for a factor asthe number of standard deviations (which may be positive or negative)that the value differs from the factor's mean value over a specifiedobservation period (e.g., over the last year). Then, one may define,e.g., a Composite Information Measure as follows:

$\begin{matrix}{{CompositeInformationMeasure} = {\sum\limits_{i}\;{Z_{i}\eta_{i}}}} & {{Equation}\mspace{14mu} 14}\end{matrix}$The Composite Information Measure (or any similar measure) is used toidentify situations in which an asset's value would have been expectedto change significantly based upon current values for the ETA® factors,in comparison to the historical means for such factors. Large positivevalues might indicate that the market value of the asset is likely toincrease (suggesting that the asset should be purchased), while largenegative values might indicate that the market value of the asset islikely to decrease (suggesting that the asset should be sold).Accordingly, an appropriate strategy would be to calculate the CompositeInformation Measure (or similar measure) for a large number of assets,identify those having high magnitudes, and then purchase or sell suchassets as indicated.

Also, certain “angle” statistics may be defined, e.g., as follows:

$\begin{matrix}{{Angle} = \frac{\Delta\;{{Model}/{Model}}}{\Delta\;{{Actual}/{Actual}}}} & {{Equation}\mspace{14mu} 15}\end{matrix}$Equation 15 calculates the percentage change in the market valueestimated using the model over a specified period of time divided by thepercentage change in the actually observed market value of the assetover the same period of time. Preferably, the subject period of time isone month or two months and, more preferably, is the immediatelypreceding one-month or two-month time period. Any model estimate may beutilized for this purpose, although it presently is preferred to useModel(2) above.

An angle statistic, such as defined in Equation 15 above, can tell aninvestor whether a subject asset is becoming relatively more overvaluedor relatively more undervalued. The analysis of such trend informationcan be helpful in determining when to purchase or sell an asset. Forexample, assume that the angle statistic defined above has been lessthan 1 for a significant period of time (indicating increasingovervaluation in the market) and is just beginning to exceed 1, in anenvironment where the asset appears to have been overvalued (e.g., basedon one of the comparison measures identified above) for a significantperiod of time. In such a case, it might be advisable to sell the asset,because the angle statistic indicates that the market is beginning toappropriately price the asset and, therefore, that its price will drop.

One also may calculate a Residual Risk Index (RRI) by calculating theaverage squared difference between the value estimated by the model andthe actually observed market value over a relevant past period of time,taking the square root of such quantity, dividing it by the average ofthe actually observed market values for the asset over the subjectperiod, and then multiplying by an appropriate Z value (e.g., from astatistical table), i.e.:

$\begin{matrix}{{RRI} = {Z*\frac{\sqrt{\frac{\sum\limits_{N}\;( {{Model} - {Actual}} )^{2}}{N}}}{\frac{\sum\limits_{N}\;{Actual}}{N}}}} & {{Equation}\mspace{14mu} 16}\end{matrix}$In the presently implemented embodiment of the invention, Z is fixed at1.96, reflecting the 96 percent confidence interval for at-distribution, and N is the total number of observations during thesubject period of time.

Any model estimate may be used in the calculation of the RRI. However,in the preferred embodiments Model(2) is utilized. In the event theasset is a portfolio, Equation 16 may be applied directly to theportfolio as a whole or else may be applied to individual assets withinthe portfolio, which then are aggregated (e.g., averaged usingvalue-weighting) in order to provide an aggregate RRI for the portfolio.Generally, it is preferable to apply Equation 16 directly to theportfolio in order to capture covariance effects that would not bereflected if the calculation separately were applied to the individualcomponents.

The RRI provides a measure of asset-specific risk that is not describedby the ETA® factors used in the corresponding model. More specifically,it measures the amount of an asset's price that is not accounted for bythe model that has been utilized. A high RRI value might indicate thatthe subject asset is a candidate for conventional asset-specificanalysis.

Conventional techniques for measuring a portfolio's error in trackingthe performance of an index typically calculate the standard deviation(or variance) of the daily differences in return between the portfolioand the benchmark, thereby effectively penalizing any deviation fromperfect tracking. This is illustrated graphically in FIG. 11A. There,the 45-degree line 360 represents ideal tracking of the index. Anydeviation 362 from it is penalized. Moreover, the penalty typicallyincreases at an increasing rate with the distance from the 45-degreeline 360.

However, the present inventors believe that sustained deviations aboveline 360, which represent better performance than the index, should notbe penalized at all. Accordingly, a better approach is to simultaneouslymeasure tracking error and performance differences. Such an approach isillustrated in the flow diagram shown in FIG. 12.

Initially, in step 390 a first asset (typically a portfolio) is modeledin relation to a second asset (typically an index being tracked). In thepreferred embodiments of the invention, such modeling is performed usinga linear or nonlinear regression of the daily returns for the portfolioagainst the daily returns for the index. An example of the result isregression line 364, shown in FIG. 11B.

Next, in step 392 the quality (or accuracy) of the model is determined.Where regression has been performed in step 390, this preferablyinvolves calculating the correlation coefficient. Such a measurementonly penalizes deviations 366 from the regression line 364, rather thandeviations from the 45-degree line 360.

In step 394, a determination is made as to whether or not the portfoliois accurately tracking the index. In the example given above, this canbe determined by examining the slope of the regression line 364 (orbeta). Ideally, it should be as close as possible to 1. In otherembodiments, other parameters of the generated model may be examined.Alternatively, if the model does not result in an express mathematicalformula (e.g., in the case of neural network modeling), the informationmay be obtained by sampling the results produced by the model (e.g., bytaking incremental samples in the region of interest).

Finally, in step 396 any under-performance or over-performance (alpha)is identified. In the example shown in FIG. 11B, the portfolio isoutperforming the index by an amount 365. It is noted that suchoutperformance would be penalized in the conventional techniques formonitoring tracking performance. Similar offset information may beobtained based on other model parameters in other embodiments. Onceagain, if the model does not result in an express mathematical formula(e.g., in the case of neural network modeling), the information may beobtained by sampling the results produced by the model (e.g., by takingincremental samples in the region of interest).

In step 398, assets are purchased or sold and/or recommendations aremade to purchase or sell assets based on the information derived fromthe preceding steps. In this regard, for example, it might be desirableto purchase additional shares of a mutual fund that is outperforming,but otherwise tracking the performance of, a particular index.Alternatively, it might be desirable to sell shares of a portfolio thatis not accurately tracking an index and also is underperforming it. Theinformation that a portfolio is not accurately tracking an index andalso is underperforming it also (or instead) might be used to trigger anadjustment to the holdings of the portfolio to more closely track thesubject index.

System Environment

Nearly all of the methods and techniques described herein can bepracticed with a general-purpose computer system. Such a computertypically will include, for example, at least some of the followingcomponents interconnected with each other, e.g., via a common bus: oneor more central processing units (CPUs), read-only memory (ROM), randomaccess memory (RAM), input/output software and/or circuitry forinterfacing with other devices and for connecting to one or morenetworks (which in turn may connect to the Internet or to any othernetworks), a display (such as a cathode ray tube display, a liquidcrystal display, an organic light-emitting display, a polymericlight-emitting display or any other thin-film display), other outputdevices (such as one or more speakers, a headphone set and/or aprinter), one or more input devices (such as a mouse, touchpad, tablet,touch-sensitive display or other pointing device; a keyboard, amicrophone and/or a scanner), a mass storage unit (such as a hard diskdrive), a real-time clock, a removable storage read/write device (suchas for reading from and/or writing to RAM, a magnetic disk, a magnetictape, an opto-magnetic disk, an optical disk, or the like), and a modem(which also may connect to the Internet or to any other computer networkvia a dial-up connection). In operation, the process steps to implementthe above methods typically are initially stored in mass storage (e.g.,the hard disk), are downloaded into RAM and then executed by the CPU outof RAM.

Suitable computers for use in implementing the present invention may beobtained from various vendors. Various types of computers, however, maybe used depending upon the size and complexity of the tasks. Suitablecomputers include mainframe computers, multiprocessor computers,workstations, personal computers, and even smaller computers such asPDAs, wireless telephones or any other appliance or device, whetherstand-alone, hard-wired into a network or wirelessly connected to anetwork. In addition, although a general-purpose computer system hasbeen described above, a special-purpose computer may also be used. Inparticular, any of the functionality described above can be implementedin software, hardware, firmware or any combination of these, with theparticular implementation being selected based on known engineeringtradeoffs. In this regard, it is noted that the functionality describedabove primarily is implemented through fixed logical steps and thereforecan be accomplished through programming (e.g., software or firmware), anappropriate arrangement of logic components (hardware) or anycombination of the two, as is well-known in the art.

It should be understood that the present invention also relates tomachine-readable media on which are stored program instructions forperforming the methods of this invention. Such media include, by way ofexample, magnetic disks, magnetic tape, optically readable media such asCD ROMs and DVD ROMs, semiconductor memory such as PCMCIA cards, etc. Ineach case, the medium may take the form of a portable item such as asmall disk, diskette, cassette, etc., or it may take the form of arelatively larger or immobile item such as a hard disk drive, ROM or RAMprovided in a computer.

The foregoing description primarily emphasizes electronic computers.However, it should be understood that any other type of computer mayinstead be used, such as a computer utilizing any combination ofelectronic, optical, biological and/or chemical processing.

Additional Considerations

Words such as “optimal”, “optimize”, “minimize”, “best” and similarwords are used throughout the above discussion. However, it should beunderstood that such words are not used in their absolute sense, butrather are intended to be viewed in light of other constraints, such asuser-specified constraints and objectives, as well as cost andprocessing constraints.

Several different embodiments of the present invention are describedabove, with each such embodiment described as including certainfeatures. However, it is intended that the features described inconnection with the discussion of any single embodiment are not limitedto that embodiment but may be included and/or arranged in variouscombinations in any of the other embodiments as well, as will beunderstood by those skilled in the art.

Similarly, in the discussion above, functionality may be ascribed to aparticular module or component. However, unless any particularfunctionality is described above as being critical to the referencedmodule or component, functionality may be redistributed as desired amongany different modules or components, in some cases completely obviatingthe need for a particular component or module and/or requiring theaddition of new components or modules. The precise distribution offunctionality preferably is made according to known engineeringtradeoffs, with reference to the specific embodiment of the invention,as will be understood by those skilled in the art.

Thus, although the present invention has been described in detail withregard to the exemplary embodiments thereof and accompanying drawings,it should be apparent to those skilled in the art that variousadaptations and modifications of the present invention may beaccomplished without departing from the spirit and the scope of theinvention. Accordingly, the invention is not limited to the preciseembodiments shown in the drawings and described above. Rather, it isintended that all such variations not departing from the spirit of theinvention be considered as within the scope thereof as limited solely bythe claims appended hereto.

1. A method for modifying a portfolio of assets to track an index ofassets, comprising: (a) identifying a set of factors having data valuesthat are correlated with an aggregate market value for the index; (b)calculating, for each of the factors, a correlative value for theportfolio relative to said each factor, thereby obtaining a correlativeprofile for the portfolio; (c) obtaining, for each of the factors, acorrelative value for the index relative to said each factor, i.e., acorrelative profile for the index; (d) calculating a measure ofdivergence between the correlative profile for the portfolio and thecorrelative profile for the index; and (e) modifying the portfolio by atleast one of buying and selling assets so as to minimize the measure ofthe divergence between the correlative profile for the portfolio and thecorrelative profile for the index, subject to any other constraints,wherein the correlative value for an item relative to a given factor isa measure of a tendency of the aggregate market value of the item tochange based on a change in the data value for said given factor.
 2. Amethod according to claim 1, wherein the set of factors includes atleast 5 factors.
 3. A method according to claim 1, wherein the set offactors includes at least 10 factors.
 4. A method according to claim 1,wherein calculating the measure of divergence in step (d) comprisescalculating a measure of correlative divergence for each factor.
 5. Amethod according to claim 1, wherein said step (e) comprisesincrementally modifying the portfolio through a sequence oftransactions.
 6. A method according to claim 5, wherein at least some ofsaid transactions are permitted to increase the measure of divergencebetween the correlative profile for the portfolio and the correlativeprofile for the index in order to achieve another user-specified goal.7. A method according to claim 5, wherein the sequence of transactionsis identified using a tree-searching technique.
 8. A method according toclaim 7, wherein a goal of each said transaction is to minimize themeasure of divergence between the correlative profile for the portfolioand the correlative profile for the index.
 9. A method according toclaim 7, wherein at least some of said transactions are permitted toincrease the measure of divergence between the correlative profile forthe portfolio and the correlative profile for the index in order toachieve another user-specified goal.
 10. A method according to claim 7,wherein said tree-searching technique comprises a step of generatingmultiple potential modifications of the portfolio.
 11. A methodaccording to claim 10, wherein said tree-searching technique furthercomprises a step of generating multiple potential subsequentmodifications for each potential modification of the portfolio.
 12. Amethod according to claim 11, wherein said tree-searching techniquefurther comprises a step of eliminating from consideration a pluralityof the multiple potential subsequent modifications, thereby resulting ina pruned tree structure.
 13. A method according to claim 1, whereinmodification of the portfolio in step (e) is limited to buying andselling assets in a pre-identified subset.
 14. A method according toclaim 13, further comprising a step of selecting the pre-identifiedsubset based on a matching of correlative profiles for different assets.15. A method according to claim 1, wherein modification of the portfolioin step (e) comprises: (1) identifying a plurality of subsets of assets;(2) identifying a transaction list for each said subset, saidtransaction list consisting essentially of purchase and/or salestransactions for the assets in said each subset; (3) for eachtransaction list, calculating the measure of divergence between thecorrelative profile for the portfolio and the correlative profile forthe index, assuming said each transaction list were executed; and (4)selecting the transaction list based on the measures of divergencecalculated in step (3).
 16. A method according to claim 15, wherein thesubsets of assets are identified in step (1) based on a matching ofcorrelative profiles for different assets.
 17. A method according toclaim 1, wherein at least one of the assets in the portfolio is cash.18. An apparatus for modifying a portfolio of assets to track an indexof assets, comprising: (a) means for identifying a set of factors havingdata values that are be correlated with an aggregate market value forthe index; (b) means for calculating, for each of the factors, acorrelative value for the portfolio relative to said each factor,thereby obtaining a correlative profile for the portfolio; (c) means forobtaining, for each of the factors, a correlative value for the indexrelative to said each factor, i.e., a correlative profile for the index;(d) means for calculating a measure of divergence between thecorrelative profile for the portfolio and the correlative profile forthe index; and (e) means for modifying the portfolio by at least one ofbuying assets, selling assets, or recommending the purchase or sale ofassets, so as to minimize the measure of the divergence between thecorrelative profile for the portfolio and the correlative profile forthe index, subject to any other constraints, wherein the correlativevalue for an item relative to a given factor is a measure of a tendencyof the aggregate market value of the item to change based on a change inthe data value for said given factor.
 19. A computer-readable mediumstoring computer-executable process steps for modifying a portfolio ofassets to track an index of assets, said process steps comprising stepsto: (a) identify a set of factors having data values that are correlatedwith an aggregate market value for the index; (b) calculate, for each ofthe factors, a correlative value for the portfolio relative to said eachfactor, thereby obtaining a correlative profile for the portfolio; (c)obtain, for each of the factors, a correlative value for the indexrelative to said each factor, i.e., a correlative profile for the index;(d) calculate a measure of divergence between the correlative profilefor the portfolio and the correlative profile for the index; and (e)modify the portfolio by at least one of buying assets, selling assets,or recommending the purchase or sale of assets, so as to minimize themeasure of the divergence between the correlative profile for theportfolio and the correlative profile for the index, subject to anyother constraints, wherein the correlative value for an item relative toa given factor is a measure of a tendency of the aggregate market valueof the item to change based on a change in the data value for said givenfactor.